Building a 21st Century Organization

The strength and versatility of the human optical system derive in wide jump from its remarkable ability to find mental synthesis and face in the substitution clear ups encoded by the retinas. To discover and let out structure, the ocular system uses a wide roam of perceptual governance mechanicss ranging from the comparatively low- aim mechanisms that underlie the fairst principles of collection and separationism, to relatively high-level mechanisms in which thickening learned associations guide the discovery of structure.The Gestalt psychologists were the send-off to fully appreciate the fundamental importance of perceptual shaping (e. g. , expect Kohler, 1947 Pomerantz & angstrom unit Kubovy, 1986). Objects a good deal appear in protestent contexts and atomic descend 18 virtu al unneuroticy never dimensiond from the same viewpoint thus, the retinal ambits associated with physical objects atomic number 18 primarily complex and varied. To get down som e(prenominal) hope of obtaining a useful exposition of the retinal images, such as recognizing objects that have been encountered previously, thither must be initial shapees that organize the image data into those roots hardly a(prenominal) similarly to change meaningful objects.Perceptual organization is also important because it ordinaryly results in highly compact images of the images, facilitating later mathematical operationing, storage, and retrieval. (See Witkin & antiophthalmic factor Tenenbaum, 1983, for a discussion of the importance of perceptual organization from the viewpoint of computational vision. ) Although much has been learned about the mechanisms of perceptual organization (see, e. g. , Beck, 1982 Bergen, 1991 Palmer & antiophthalmic factor Rock, 1994 Pomerantz & adenine Kubovy, 1986), progress in developing examinationable three-figure theories has been slow. iodine bea where substantial progress has been made is in mystifys of texture sort and separatism. These models have begun to put the study of perceptual organization on a firm suppositional footing that is consistent with the psychophysics and physiology of low-level vision. Two command types of model for texture segregation have been proposed. In the feature-based models, retinal images be initially processed by mechanisms that find specific features, such as edge segments, line segments, blobs, and terminators. classify and segregation are hence accomplished by finding the image regions that contain the same feature or bunch of features (see, e. g. , Julesz, 1984, 1986 Marr, 1982 Treisman, 1985). These models are relatively primary, are consistent with more or less aspects of low-level vision, and have been able to account for a concatenation of experimental results. In the filter-based models, retinal images are initially processed by tuned take, for ex group Ale, contrast-energy channels selective for sizing of it and penchant. mathematical group an d segregation are then accomplished by finding those image regions with approximately constant output from genius or to a greater extent channels (Beck, Sutter, & ampere Ivry, 1987 Bergen & Landy, 1991 Bovik, Clark, & Geisler, 1990 Caelli, 1988 Chubb & Sperling, 1988 Clark, Bovik, & Geisler, 1987 Fogel & Sagi, 1989 Graham, Sutter, & Venkatesan, 1993 Victor, 1988 Victor & Conte, 1991 Wilson & Richards, 1992).These models have some advantages over the alive feature-based models They lowlife be applied to imperious images, they are commonplacely to a greater extent consistent with known low-level mechanisms in the visual system, and they have prove capable of accounting for a wider range of experimental results. However, the current models do not make accurate predictions for certain important classes of stimuli. One class of stimuli are those that contain regions of texture that can be segregated unless on the basis of local anaesthetic structure (i. e . , shape).Another broad class of stimuli for which close current perceptual organization models do not make equal predictions are those containing nonstationary structures specifically, structures that change smoothly and systematically crossways space. Nonstationary structures are the general rule in natural images because of perspective projection, and because many other(prenominal) natural objects are the result of some irregular growth or erosion process. A dim-witted example of a nonstationary structure would be a con nervous straination formed by a sequence of line segments (a dashed constellation) enter in a background of randomly oriented line segments.Such contours are usually easily picked out by human observers. However, the elements of the contours cannot be separate by the mechanisms contained in current filter-based or feature-based models, because no single orientation channel or feature is activated across the whole contour. Grouping the elements of such co ntours involves some kind of contour integration process that binds the attendant contour elements together on the basis of local resemblance. A more complex example of a nonstationary structure would be an image of woodwind instrument grain.Such a texture contains many contours whose spacing, orientation, and curvature vary smoothly across the image. Again, such textures are easily grouped by human observers scarcely cannot be grouped by the mechanisms contained in the current models. Grouping the contour elements of such textures requires some form of texture integration (the two-dimensional line of latitude of contour integration). The heart of the problem for existing quantitative models of class and segregation is that they do not move the structure of the image data with the splendor achieved by the human visual system.The human visual system ostensibly represents image t severallying in an elaborate hierarchical fashion that captures many of the spacial, temporal, and chromatic relationships among the entities grouped at each level of the hierarchy. Grouping and segregation based on simple feature distinctions or channel responses whitethorn substantially be an important initial comp integritynt of perceptual organization, solely the final organization that come forths must depend on more advance(a) processes.The major theoretical aim of this study was to develop a example for constructing and testing models of perceptual organization that capture some of the richness and complexness of the representations extracted by the human visual system, and yet are computationally well moldd and biologically possible. Within this framework, we have developed a model of perceptual organization for two-dimensional (2D) line images and evaluated it on a number of textbook perceptual organization demonstrations.In this article we refer to this model as the broad model when it is necessary to distinguish it from a simplified translation, the restri ct model, depict later. Perceptual organization must depend in some way on obtained similarities and oddments between image elements. Furthermore, it is obvious that similarities and disagreements along many varied arousal dimensions can contribute to the organization that is perceived. Although in that respect have been many studies of individual stimulus dimensions, there have been few systematic attempts to study how multiple dimensions interact (Beck et al., 1987 Fahle & Abele, 1996 Li & Lennie, 1996). The major experimental aim of this study was to measure how multiple stimulus dimensions are combined to determine radical strength between image elements. To this end, we conducted a series of three-pattern assort experiments to directly measure the tradeoffs among two, three, or quadruple stimulus dimensions at a time. Predictions for these experiments were generated by a restricted version of the model appropriate for the experimental task. The experimental resu lts provided both a test for the restricted model and a means of estimating the models parameters.The estimated parameter values were employ to generate the predictions of the extended model for complex patterns. The next four sections describe, respectively, the theoretical framework, the restricted model, the experiments and results, and the extended model and demonstrations. Theoretical Framework for Perceptual organization In this section we discuss four important components of perceptual organization hierarchical representation, detection of primitives, detection of similarities and differences among image better, and mechanisms for grouping image parts.These components interpreted together form the theoretical framework on which the restricted and extended quantitative models are based. Hierarchical Representation It is evident that the mechanisms of perceptual organization yield a rich hierarchical representation that describes the relationship of parts to wholes at a nu mber of levels that is, the wholes at one level often become the parts at the next level. However, there is evidence that the process by which the hierarchical representation is constructed does not proceed strictly either from local to global or from global to local.The global structure of a large letter composed of dwarfish letters can be observed originally the structure of the individual small letters is discovered (Navon, 1977), and there exist ambiguous figures, such as R. C. Jamess classic Dalmatian dog, that can be solved locally whole after at least some of the global structure is discovered. On the other hand, the discovery of structure must sometimes proceed from local to global for example, it would be hard to extract the symmetry of a complex object without initiatory extracting some of the structure of its subobjects.Any well-specified theory of perceptual organization must define what is meant by parts, wholes, and relationships between parts and wholes. Given the current state of knowledge, all definitions, including the ones we have adopted, must be tentative. Nonetheless, some basic definitions must be made in come out to form working models. In our framework, the most primitive objects are defined on the basis of the current discernment of image encoding in the elemental visual cortex of the hierarch visual system.Higher aim objects are defined to be collections of lower order objects (which may include primitive objects), together with randomness about the relationships between the lower order objects. The range of relationships that the visual system can discover, the order and speed with which they are discovered, and the mechanisms utilise to find them are unsettled issues. As a starting point the relationships we consider are quantitative similarities and differences in size, position, orientation, color, and shape.These dimensions were picked for historical and intuitive reasons They are major categories in human actors line and therefore are likely to correspond to perceptually important categories. The little definitions of these dimensions of similarity between objects are given later. Detection of Primitives Receptive-Field Matching One of the simplest mechanisms for detecting structure within an image is receptive-field interconnected, in which relatively hard-wired circuits are used to detect the different spatial patterns of interest.For example, simple cells in the primary visual cortex of monkeys behave approximately like hard-wired templates A safe response from a simple cell indicates the presence of a local image pattern with a position, orientation, size (spatial frequency), and phase (e. g. , even or odd symmetry) similar to that of the receptive-field profile (Hubel & Wiesel, 1968 for a review, see DeValois & DeValois, 1988). The complex cells in the primary visual cortex are another example.A strong response from a typical complex cell indicates a particular position, orien tation, and spatial frequency independent of the spatial phase (Hubel & Wiesel, 1968 DeValois & DeValois, 1988). Receptive field interconnected may occur in areas other than the primary visual cortex, and may involve detection of image structures other than local luminance or chromatic contours, for example, structures such as phase discontinuities (von der Heydt & Peterhans, 1989) and simple radially symmetric patterns (Gallant, Braun, & van Essen, 1993).An important aspect of receptive-field better halfing in the visual cortex is that the information at each spatial location is encoded by a large number of neurons, each selective to a particular size or scale. The population as a whole spans a wide range of scales and hence provides a multiresolution or multiscale representation of the retinal images (see, e. g. , DeValois & DeValois, 1988). This multiresolution representation may play an important role in perceptual organization.For example, grouping of low-reso lution information may be used to constrain grouping of high-resolution information, and vice versa. The quantitative models described here assume that receptive-field co-ordinated provides the primitives for the subsequent perceptual organization mechanisms. However, to hold down the complexity of the models, the receptive-field interconnected stage is restricted to include only units similar to those of cortical simple cells with small receptive fields. These units proved sufficient for the line pattern stimuli used in the experiments and demonstrations.Receptive-field co-ordinated is practical only for a few classes of simple image structure, such as contour segments it is unreasonable to suppose that there are hard-wired receptive fields for every image structure that the visual system is able to detect, because of the combinatorial explosion in the number of receptive-field shapes that would be required. Thus, there must be additional, more flexible, mechanisms for detecting s imilarities and differences among image regions. These are discussed next. Similarity/Difference Detection MechanismsStructure exists within an image if and only if some systematic similarities and differences exist between regions in the image. Thus, at the heart of any perceptual organization system there must be mechanisms that adjoin or compare image regions to detect similarities and differences. (For this discussion, the reader may have in mind of image regions as either parts of an image or as groups of detected primitives. ) Transformational co-ordinated A long-familiar general method of comparison image regions is to find out how well the regions can be mapped onto each other, given certain allowable transformations (see, e.g. , Neisser, 1967 Pitts & McCulloch, 1947 Rosenfeld & Kak, 1982 Shepard & Cooper, 1982 Ullman, 1996). The predilection is, in effect, to use one image region as a transformable template for comparison with another image region. If the regio ns closely match, next application of one of the allowable transformations, then a certain similarity between the image regions has been detected. Furthermore, the specific transformation that produces the closest match provides information about the differences between the image regions.For example, consider an image that contains two groups of small line segment primitives detected by receptive-field matching, such that each group of primitives forms a triangle. If some particular translation, rotation, and scaling of one of the groups brings it into perfect junction with the other group then we would know that the two groups are identical in shape, and from the aligning transformation itself we would know how much the two groups differ in position, orientation, and size. There are many possible versions of transformational matching, and thus it represents a broad class of similarity-detection mechanisms.Transformational matching is also very powerfulthere is no relationship be tween two image regions that cannot be described given an appropriately general set of allowable transformations. Thus, although there are other plausible mechanisms for detecting similarities and differences between image regions (see section on attribute matching), transformational matching is general enough to serve as a useful starting point for developing and evaluating quantitative models of perceptual organization. rehearse of both spatial position and colorThe most obvious form of transformational matching is based on standard template matching that is, maximizing the correlation between the two image regions under the family of allowable transformations. However, template matching has a well-known limitation that often produces undesirable results. To understand the problem, distinction that each point in the two image regions is described by a position and a color. The most general form of matching would consist of canvas both the positions and colors of the points. How ever, standard template matching compares only the colors (e. g. , gray levels 2 ) at like positions.If the points cannot be lined up in space then large match errors may occur even though the positional errors may be small. A more useful and plausible form of matching mechanism would treat spatial and color information more equivalently by comparing both the spatial positions and the colors of the points or parts reservation up the objects. For such mechanisms, if the colors of the objects are identical then similarity is indomitable solely by how well the spatial coordinates of the points or parts reservation up the objects can be aligned and on the values of the spatial transformations that bring them into the best possible alignment.In other words, when the colors are the same, then the matching error is described by differences in spatial position. For such mechanisms, B matches A better than B matches C, in agreement with intuition. after we describe a simple matching mecha nism that simultaneously compares both the spatial positions and the colors of object points. We show that this mechanism produces matching results that are generally more perceptually sensible than those of template matching. Attribute matchingAnother well-known method of comparing groups is to measure various attributes or properties of the groups, and then represent the differences in the groups by differences in the measured attributes (see, e. g. , Neisser, 1967 Rosenfeld & Kak, 1982 Selfridge, 1956 Sutherland, 1957). These attributes might be simple measures, such as the mean and variance of the color, position, orientation, or size of the primitives in a group, or they might be more complex measures, such as the invariant shape moments. It is likely that perceptual organization in the human visual system involves both transformational matching and attribute matching.However, the specific models considered here involve transformational matching exclusively. The primary reas on is that perceptual organization models based on transformational matching have relatively few free parameters, yet they are sensitive to differences in image structurean requisite requirement for moving beyond existing filter- and feature-based models. For example, a simple transformational matching mechanism (described later) can detect small differences in arbitrary 2D shapes without requiring an explicit description of the shapes.On the other hand, specifying an attribute-matching model that can detect small differences in arbitrary shapes requires specifying a set of attributes that can describe all the relevant details of arbitrary shapes. This type of model would require many assumptions and/or free parameters. Our current view is that transformational matching (or something like it) may be the central mechanism for similarity/difference detection and that it is supplemented by certain forms of attribute matching. Matching groups to categoriesThe discussion so outlying(pr enominal) has assumed implicitly that transformational and attribute matching occur between different groups extracted from the image. However, it is obvious that the brain is also able to compare groups with stored information because this is essential for memory. Thus, the visual system may also measure similarities and differences between groups and stored categories, and coiffure subsequent grouping using these similarities and differences. These stored categories might be represented by prototypes or sets of attributes.Rather than use stored categories, the visual system could also measure similarities and differences to categories that emerge during the perceptual processing of the image. For example, the visual system could extract categories corresponding to prevalent colors within the image, and then perform subsequent grouping on the basis of similarities between the colors of image primitives and these emergent color categories. Grouping Mechanisms Once similarities and differences among image parts are discovered, then the parts may be grouped into wholes.These wholes may then be grouped to form larger wholes, resegregated into a different collection of parts, or both. However, it is important to observe in mind that some grouping can occur in front all of the relevant relationships between the parts have been discovered. For example, it is possible to group together all image regions that have a similar color, before discovering the geometrical relationships among the regions. As further relationships are discovered, the representations of wholes may be enriched, sore wholes may be formed, or wholes may be broken into bare-ass parts and reformed.Thus, the discovery of structure is likely to be an asynchronous process that operates simultaneously at multiple levels, often involving an elaborate interleaving of similarity/difference detection and grouping. Within the theoretical framework proposed here we consider one grouping constraintthe gen eralized uniqueness principleand three grouping mechanisms transitive grouping, nontransitive grouping, and multilevel grouping. The uniqueness principle and the grouping mechanisms can be applied at multiple levels and can be interleaved with similarity/difference detection.Generalized uniqueness principle The uniqueness principle proposed here is more general it enforces the constraint that at any time, and at any level in the hierarchy, a given object (part) can be assigned to only one superordinate object (whole). An object at the lowest level (a primitive) in the hierarchy can be assigned to only one object at the next level, which in turn can be assigned to only one object at the next level, and so on. The sequence of nested objects in the hierarchy containing a given object is called the partwhole path of the object.The generalized uniqueness principle, if valid, constrains the possible perceptual organizations that can be found by the visual system. Nontransitive grouping Ou r working shot is that similarity in spatial position (proximity) contributes weakly to nontransitive grouping. If proximity were making a dominant contribution, then separated objects could not bind together separately from the background objects. 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